Figuring out whether to take a lump sum or an annuity from a lottery is a great problem to have. Ultimately, it comes down to whether you'd like to get a whole lot of free money right now or a lot of free money every year for a long time. However, the two types of payments have some fundamental differences and, if you hit a big jackpot, the difference could work out to millions of dollars.

Winning the Lottery

Imagine for a minute that your lucky numbers match the jackpot for a lottery and you win. For example, if you were to hit a Mega Millions jackpot, you might get a choice between $48.4 million now or $87 million spread out over 30 years. While 30 payments of $2.9 million each add up to a lot more money than $48.4 million now, it might not be the better deal.

Time Value of Money

Money today is usually worth more than money tomorrow. This is why the lottery's lump sum payments are less than the sum of the amount of money that you'd get in payments over time. One way to think about the difference between the two is to look at the lump sum amount as your actual winnings. Once you do that, the question becomes whether or not you can invest that lump sum in a way that gets you more money over 30 years than the annuity option. If you can, you do better to take the lump sum, at least from a financial perspective.

Benefit and Danger of Annuities

Choosing the annuity method has a key benefit. It saves you from having to budget your money, since you know that you'll be getting the payments from the lottery for a long period of time. However, it also carries a significant risk. Some day, your payments will stop, and if you haven't saved money, your life could change a great deal. For instance, if you win the lottery when you're 21 and you get 30 years' worth of $2.9 million payments, your annuity stream will stop when you're 51, which isn't that long before you want to retire. Going from $2.9 million in income per year to $0 can be pretty shocking, whether or not you plan to retire.

Investing Your Lump Sum

Taking the lump sum could be a great opportunity -- or it could leave you broke. Unfortunately, many lottery winners blow their winnings. However, if you invest them, you could not only have ample income, but also obtain true wealth that could last for your lifetime and beyond.

For example, you could take your $48.4 million and invest it in a conservative portfolio returning 6.5 percent, which is below the stock market's historical 10 percent annual return. If you did this, you could take out $2.9 million per year indefinitely, and your portfolio would keep growing. If you want to increase your payments by 2 percent per year for inflation, your money would last 39 years if you started with a $2.5 million withdrawal and gradually increased it to $5.3 million. Investing it at 7.5 percent, which is still relatively conservative, would make it last 88 years.